Redo armature without stacking modifications?
You need to apply the new pose of the armature as its rest pose before adding the modifier to the mesh. The mesh is deformed by the armature by using the difference between the armature's current pose (what is set in pose mode) and its rest pose (what you see in edit mode on the armature).

In pose mode, under the "Pose" menu, select "Apply Pose as Rest Pose". This will make the pose mode position of your armature become its edit mode position.